Question

In the figure, $O$ is the centre of the circle with radius $13cm$. $OP\perp AB$, $OQ\perp CD$, $AB\parallel CD$
$AB=24cm$ and $CD=20cm$. Determine $PQ$.

Answer 1

$O{P}^2+P{A}^2=O{A}^2$

$\therefore O{P}^2+144=169$

$\therefore OP=5$ ...(i)

$O{C}^2=O{Q}^2+C{Q}^2$

$\Rightarrow 169=O{Q}^2+100$

$\Rightarrow OQ=\sqrt{69}$ ...(ii)

$PQ=PO+OQ$

$PQ=5+\sqrt{69}$